Darrell Williamson

Block decision feedback equalization

A natural generalization of the conventional decision feedback equalizer (DFE) based on block processing and maximum a posteriori decisions is presented. This block DFE is indexed by two parameters depending on the block length p and the number of decisions q >

Roundoff noise minimization and pole-zero sensitivity in fixed-point digital filters using residue feedback

The problem of designing a finite wordlength fixed-point realization of an Nth-order digital filter, which uses residue feedback to minimize the output roundoff noise subject to l 2 -scaling, is considered. The new structures require N extra additions, but no more multiplications than the earlier low noise structures of Mullis and Roberts, and have lower roundoff noise for sufficiently narrow bandwidth filters. A new set of filter invariants, called the residue modes, are defined which characterize the new low noise structures and determine the output noise variance. If the sum of the residue modes is less than the sum of the second-order modes of Mullis and Roberts, then lower roundoff noise is achieved. Every filter structure is shown to define a unique (symmetrizing) matrix Q. Pole-zero sensitivities and a new noise measure are defined in terms of Q. Numerical results are included which compare the noise and pole-zero sensitivity characteristics of different filter structures.

Delay replacement in direct form structures

A class of high-order low-sensitivity digital filter structures is generated by means of a direct transformation of a high-order direct-form (DF) structure. The proposed structures have low coefficient dynamic range, and exhibit low coefficient frequency-response sensitivity and roundoff noise characteristics, yet require only 3N multiplications per output sample as compared to 2N in the direct-form case. >

Residue feedback in digital filters using fractional feedback coefficients

A residue feedback network for recursive digital filter structures is proposed in which the total residue is split into two parts (bits sliced) and processed by separate feedback networks. These networks can be implemented with less hardware compared to conventional methods of implementing extended precision arithmetic giving the same SNR, and they lead to improved limit cycle behavior.

Stability of impulsive dynamical systems

The paper considers an extension of LaSalles invariance principle for the investigation of the stability of an impulsive dynamical system. In particular, we show that the existence of non-increasing Lyapunov function is not sufficient for stability, but that an extra condition on the impulsive vectors is required which depends on both the magnitude and the direction of the impulsive vectors.

Discrete event reference control

We consider a new approach to improve the performance of reference tracking problems for closed loop stabilized continuous linear systems through manipulation of the reference signals initiated by the occurrence of a discrete event. By means of the internal model principle, we show that a change in the reference signal is equivalent to implementing an instantaneous change via the choice of a decision vector in the state of the reference model. The analysis of the resulting hybrid discrete event reference control system is then shown to be equivalent to the analysis of a linear impulsive system. In particular, it is shown how decision vectors are chosen to achieve a deadbeat tracking error response.

Dynamically scaled fixed point arithmetic

A technique is presented for dynamically scaling a fixed-point filter at each stage of the iteration such that overflow is no more likely than when floating point arithmetic is used. The results are a generalization of earlier work.<<ETX>>

Structural state space sensitivity in linear systems

Abstract The concept of transformation independent noise is introduced to define a general class of structurally insensitive state space realizations of a given transfer function. A performance measure is minimized subject first to only an t 2 -scaling constraint on the norm of each state node. This constraint normalizes the contribution of each state in the performance measure. Later additional constraints are imposed on the class of allowable state space structures. One constraint requires a covariance decoupled structure while another imposes a constraint on the Markov parameters of a partitioned substructure.

On the Convergence of Sampled Data Nonlinear Systems

The effect of sampling on the convergence of closed loop continuous systems is investigated. The systems under consideration are nonlinear containing parameter uncertainties. It is shown that the discretized of a converging controller results in convergence of the sampled data closed loop system; i.e., a nonlinear continuous-time system subject to a discrete controller; if the sampling time is in an open set and the continuous plant satisfies certain Lipschitz type conditions. The results are derived for both global and local convergences.

Error feedback in a class of orthogonal polynomial digital filter structures

A method of applying error feedback in three digital ladder and lattice filter structures derived from the theory of orthogonal polynomials is proposed. It is shown that error feedback leads to significant improvement in both the roundoff noise characteristics and limit cycle behavior. In particular, the error-compensated one-multiplier structure is superior to the (uncompensated) normalized ladder. This results in significant savings in both hardware and Speed of implementation.